Method and Apparatus for Precision Phasor Measurements Through a Medium-voltage Distribution Transformer

ABSTRACT

A means and method for measuring precise voltage phasors on medium-voltage alternating current (AC) distribution grids, using existing distribution transformers as voltage sensors. The errors introduced by the distribution transformers are minimized by taking into account the transformer&#39;s vector impedance, combined with measuring the transformer secondary current phasor. The invention includes a means and a method of measuring the distribution transformer&#39;s vector impedance.

CROSS-REFERENCE TO RELATED APPLICATIONS

Not Applicable

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

The invention disclosed herein was conceived and developed in partduring work on Award Number DE-AR0000340, titled “Micro-Synchrophasorsfor Distribution Systems,” from the Advanced Research ProjectsAgency-Energy (ARPA-E) of the U.S. Department of Energy.

REFERENCE TO SEQUENCE LISTING, A TABLE, OR A COMPUTER PROGRAM LISTINGCOMPACT DISK APPENDIX

Not Applicable

BACKGROUND OF THE INVENTION

The present invention is in the technical field of measurement ofelectric parameters. More particularly, the present invention is in thetechnical field of voltage phase angle measurements on an alternatingcurrent (a.c.) power grid.

The voltage and current on an a.c. power grid have a fundamentalfrequency, often one of the following: 50 Hertz, 60 Hertz, or 400 Hertz.For many applications, it can be useful to measure the phase angle ofthe voltage fundamental frequency, or the phase angle of the currentfundamental frequency, or both. Such a measurement can be made eitherrelative to the phase angle at a different physical location, orrelative to a fixed time base such as that provided by the GlobalPositioning System. The measured fundamental angle can be combined withthe measured fundamental magnitude to form a phasor measurement.

Phasor measurements can be equivalently expressed in polar coordinates,as an angle and a magnitude; or they can be expressed in Cartesiancoordinates, typically for a.c. systems as a real and an imaginarycomponent; or they can be expressed as a vector on a rotating Cartesiancoordinate system that completes one rotation per nominal fundamentalcycle; or they can be expressed in any other mathematically-equivalentway.

One known phasor application for a.c. grids, well known to thosefamiliar with the art, is the synchrophasor application, in which thevoltage phasor, current phasor, or both are examined simultaneously attwo or more separate physical locations on an a.c. grid that connectsthose two or more locations. In this known application, the differencebetween phasors at the two separate physical locations may, for example,provide useful information about the power flow between those twolocations.

In a.c. power grids, it is common to refer to voltages above 100,000volts as high-voltage, and voltages between 1,000 volts and 100,000volts as medium-voltage, and voltages less than 1,000 volts aslow-voltage. High-voltage is generally used in an a.c. grid fortransmitting bulk power over long distances; this application is oftenreferred to as a transmission system. Medium-voltage is generally usedin an a.c. grid for distributing power from a substation to a locationthat is closer to end-use; this application is often referred to as adistribution system. Low-voltage is generally used in an a.c. grid byend users or consumers, such as residences, factories, and commercialfacilities.

Typically, synchrophasor applications have been applied to high-voltagepower transmission systems, even if the measurements themselves are madeon local low-voltage locations.

In those synchrophasor applications on transmission systems, thedifference in phase angle between two separate physical locations canoften be tens of degrees or more, and detecting interesting phenomenararely requires a resolution better than about half a degree. Indeed,the IEEE Standard C37.118 (2011) for synchrophasor measurements onlyrequires a Total Vector Error of 1% or better, which corresponds toapproximately ±0.5°.

In our Department of Energy ARPA-E Project DE-AR0000340, titled“Micro-Synchrophasors for Distribution Systems,” we have beeninvestigating the application of synchrophasor measurements tomedium-voltage distribution grids, as opposed to the traditionalapplication to high-voltage transmission grids. Due to smallerinductances and shorter distances on distribution grids compared totransmission grids, the phase angle changes during interesting phenomenaon distribution grids are much smaller. We have determined that, fordistribution grid applications, a angular resolution for voltage phasorsand current phasors of ±0.015° could be useful.

Transmission grids generally operate at 100,000 volts or higher, anddistribution grids generally operate at 1,000 volts to 100,000 volts. Asis well known in the art, to measure a.c. voltage on these grids it isnecessary to proportionally reduce the a.c. voltage to an acceptablelevel for electronic devices, which conventionally measure signals thatare less than 1,000 volts.

Typically, this proportional voltage reduction is done withtransformers. One commonly-available type of transformer, which we willcall a distribution transformer, is intended to supply a significantamount of power to a load, such as a group of residences or a factory,but can also be used for making phasor measurements. The medium-voltageprimary winding of distribution transformers is connected to thedistribution grid; the low-voltage secondary winding delivers power toconsumers, and is at a level that can be measured by electronic devices.

In general, we are interested in making phasor measurements thatindicate the voltage magnitudes and angles on the distributionconductors, but as a practical matter we instead measure the voltagephasors on the secondary windings of a transformer.

Consequently, any phase angle shifts that occur inside the transformer,between the primary winding and the secondary winding, will affect theaccuracy and resolution of a voltage phasor measurement.

Prior to the present invention, it was believed by those familiar withthe art that high-precision medium-voltage phasor measurements, usinggenerally available distribution transformers, would be impossible. Itis well known to those familiar with the art that the voltage phasor onthe secondary winding of distribution transformers, where themeasurement would take place, is strongly affected by the uncontrolledloads that are supplied by the secondary winding of a distributiontransformer.

SUMMARY OF THE INVENTION

The present invention is a means and a method for making precise voltagephasor measurements on medium-voltage conductors of a distribution grid,using measurements that are made on the secondary of an existingdistribution transformer that is supplying power to loads.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustration of the environment of the present invention.

FIG. 2 is a schematic view of the key elements of FIG. 1.

FIG. 3 is a view of one implementation of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Turning our attention to FIG. 1, we see distribution grid conductors 1mechanically supported by a power pole 2. Mounted on the power pole 2 isa transformer 3. The transformer 3 could, for example, be a single-phasetransformer having a ratio of 100:1 for converting 24 kilovolts on itsprimary winding to 240 volts on its secondary winding. Themedium-voltage primary winding of the transformer 3 is connected throughprimary conductors 9 and a fuse 10 to the medium-voltage distributiongrid conductors 1. The low-voltage secondary winding of the transformer3 is connected through secondary conductors 4 to conductors 5 on alow-voltage distribution grid. In FIG. 1, we see an enclosure 6 for thepresent invention. The present invention, inside its enclosure 6, makesuse of current sensors 7 on the secondary conductors 4, and also makesuse of voltage sensing conductors 8, to make measurements of voltagephasors and current phasors on the low voltage secondary of transformer3. These measured secondary voltage phasors and current phasors are usedin the present invention to precisely determine the voltage phasors onthe medium-voltage distribution grid conductors 1, as further describedbelow.

Turning our attention now to FIG. 2, we see, in schematic form, many ofthe same elements that we saw in FIG. 1: distribution grid conductors 1,a transformer 3, primary conductors 9, a fuse 10, secondary conductors4, conductors 5 on a low-voltage distribution grid, an enclosure 6 forthe present invention, current sensors 7 on the secondary conductors 4,and voltage sensing conductors 8. We also see a Micro SynchrophasorInstrument 31, developed under the Department of Energy ARPA-E AwardNumber DE-AR0000340, which implements one possible embodiment of thepresent invention. The Micro Synchrophasor Instrument 31 has voltageinputs 35 with appropriate ratings for direct connection to thelow-voltage secondary winding of the transformer 3, and has currentinputs 34 with appropriate ratings for using current sensors 7 tomeasure the current flowing on the low-voltage secondary conductors 4.

Turning our attention now to FIG. 3, we see an illustration of a MicroSynchrophasor Instrument 31 which implements one possible embodiment ofthe present invention. (The hand 37 in the illustration is shown tovisually indicate approximate scale, and does not play any part in thepresent invention.) The Micro Synchrophasor Instrument 31 incorporates adisplay 33 and communications means 36, both of which are useful but notcritical to the present invention. The Micro Synchrophasor Instrument 31also incorporates voltage inputs 35 for measuring the low-voltagephasors on the secondary winding of the transformer 3, current inputs 34for measuring the current flowing on the secondary conductors throughcurrent sensors, and computing means 32 for implementing the algorithmof the present invention, which is further described below.

In the present invention, we use measurements on the secondary,low-voltage conductors of a distribution transformer to preciselydetermine the voltage phasors on the primary, medium-voltagedistribution grid conductors, which is also the voltage on the primaryof the transformer, using the method explained further below.

We begin by making voltage phasor measurements and current phasormeasurements on the secondary, low-voltage conductors, using any precisemethod known in the art. Combining these secondary voltage phasormeasurements and secondary current phasor measurements with theeffective ratio of the transformer primary winding to the transformersecondary winding, which can be found on the transformer nameplate, weimplement the following equation to determine the parameter we want tomeasure: the phasor vector of the fundamental voltage on the primarywinding of the transformer.

{right arrow over (V)} _(primary)=α_(transformer)·({right arrow over(V)} _(secondary)+({right arrow over (I)} _(secondary) ·{right arrowover (Z)} _(transformer)))

V_(primary) is the phasor vector of the fundamental voltage on theprimary winding of the transformer, which is the parameter of interest;

α_(transformer) is the effective ratio of the transformer primarywinding to the transformer secondary winding;

V_(secondary) is the measured phasor vector of the fundamental voltageon the secondary side of the transformer;

I_(secondary) is the measured phasor vector of the fundamental currenton the secondary side of the transformer; and

Z_(transformer) is the fundamental vector impedance of the transformer,as further described below.

Note that this equation requires that we know the fundamental vectorimpedance of the transformer.

In our invention, we measure the fundamental vector impedance of thetransformer by observing the changes in our secondary voltage phasormeasurements that occur simultaneously with changes in our secondarycurrent phasor measurements. We approximate the relationship betweenthose two measurements and the fundamental vector impedance of thetransformer as follows:

${\overset{\rightarrow}{Z}}_{transformer} \cong \frac{\Delta \; {\overset{\rightarrow}{V}}_{secondary}}{\Delta \; {\overset{\rightarrow}{I}}_{secondary}}$

ΔV_(secondary) is the measured phasor vector of a change in fundamentalvoltage on the secondary side of the transformer, and

ΔI_(secondary) is the measured phasor vector of a change in fundamentalcurrent on the secondary side of the transformer.

As shown in this equation, the fundamental vector impedanceZ_(transformer) can be approximated by analyzing the measured vectorchange in secondary voltage that occurs approximately simultaneouslywith a detected vector change in the measurement of secondary current.It is an approximation of the fundamental vector impedanceZ_(transformer) for two reasons. First, the measured fundamental vectorimpedance is, in fact, the vector impedance of the transformer summedwith the vector impedance of the grid that is upstream of thetransformer primary; however, we have determined by experiment that thetransformer vector impedance is almost always at least an order ofmagnitude larger than the upstream grid's vector impedance. Second,there can be changes in measured phasor vector of the fundamentalvoltage on the secondary side of the transformer that are caused byexternal factors other than changes in the phasor vector in thefundamental current on the secondary side of the transformer, suchexternal factors including voltage sags on the primary, transformer tapchanges, and other well-known events that affect transformer secondaryvoltage.

To minimize the effect of these kinds of external factors, in ourinvention the approximation of the fundamental vector impedanceZ_(transformer) may be calculated directly as described above, or it maybe further refined using one or more of the following three methods:

-   -   Threshold: For the purposes of calculating Z_(transformer),        changes in ΔV_(secondary) are ignored unless they occur        simultaneously with a change in ΔI_(secondary) that exceeds some        threshold in vector magnitude, or exceeds some threshold in some        parameter associated with the current phasor such as its real        component or its imaginary component. This threshold may be        fixed, or it may be determined by an algorithm that adapts this        threshold to a history of measurements.    -   Statistical correlation: For the purposes of calculating        Z_(transformer), which is in the present invention is        approximated by a ratio, a statistical correlation may be used        to calculate the most likely ratio between a large number of        measured changes in ΔI_(secondary) and a change in        ΔV_(secondary). For example, the slope of a linear least-squares        fit could be used; or a statistical process that gives more        weight to points that have a large change in current phasor        could be used; or any other statistical method known to those        familiar with the art could be used to extract an optimal ratio        from a collection of ΔI_(secondary) and ΔV_(secondary) pairs.    -   Intentional change in secondary current vector: the present        invention relies on changes in ΔI_(secondary), which almost        always naturally occur in distribution transformer loads. In one        implementation of the present invention, a measurement of        Z_(transformer) can be made by intentionally adding and removing        load from the secondary of the distribution transformer. In        another embodiment, the adding and removing are done in a timed        pattern that permits extraction of relatively small signals from        background noise using methods well-known in the art, such as        fixed-frequency adding and removing combined with Fourier        analysis; or random adding and removing combined with        auto-correlation.

It will be apparent to one of ordinary skill that the above description,which assumes a single-phase system, can be readily extended tothree-phase systems.

While the foregoing written description of the invention enables one ofordinary skill to make and use what is considered presently to be thebest mode thereof, those of ordinary skill will understand andappreciate the existence of variations, combinations, and equivalents ofthe specific embodiment, method, and examples herein. The inventionshould therefore not be limited by the above described embodiment,method, and examples, but by all embodiments and methods within thescope and spirit of the invention.

1-9. (canceled)
 10. An apparatus for measuring a phasor vector of afundamental primary voltage applied to a primary winding of analternating current transformer, said apparatus using only measurementson a secondary winding of the alternating current transformer, saidfundamental primary voltage having a magnitude between 1,000 volts and100,000 volts, said transformer having a fundamental secondary voltagemagnitude less than 1,000 volts, said transformer having a transformer'seffective ratio equal to the fundamental primary voltage magnitudedivided by the fundamental secondary voltage magnitude; said secondarywinding connected to a secondary load that draws a fundamental secondarycurrent, said fundamental secondary current not being constant in time;said transformer having a transformer's fundamental vector impedance;said apparatus making a plurality of measurements of the fundamentalsecondary voltage and a plurality of simultaneous measurements of thefundamental secondary current, then using the plurality of measurementsof the fundamental secondary current to calculate a plurality of phasorvectors of change in the secondary fundamental current, and using theplurality of measurements of the fundamental secondary voltage tocalculate a plurality of phasor vectors of change in the secondaryfundamental voltage, the plurality of phasor vectors of change in thesecondary fundamental voltage being substantially simultaneous in timewith the plurality of phasor vectors of change in the secondaryfundamental current; said apparatus using an algorithm to calculate thetransformer's fundamental vector impedance from the relationship betweenthe plurality of phasor vectors of change in secondary fundamentalcurrent and the plurality of simultaneous phasor vectors of change inthe secondary fundamental voltage; said apparatus producing ameasurement of the phasor vector of the fundamental primary voltage by:measuring the phasor vector of the fundamental secondary voltage;measuring the phasor vector of the fundamental secondary current;calculating an adjusted phasor vector of the fundamental secondaryvoltage by vector-summing the measured phasor vector of the fundamentalsecondary voltage with the vector-product of the measured phasor vectorof the fundamental secondary current and the transformer's fundamentalvector impedance; producing a measurement of the phasor vector of thefundamental primary voltage by multiplying the adjusted phasor vector ofthe fundamental secondary voltage by the transformer's effective ratio.10. The apparatus of claim 10 in which the algorithm to calculate thetransformer's fundamental vector impedance from the plurality of phasorvectors of change in secondary fundamental current and the plurality ofsimultaneous phasor vectors of change in the secondary fundamentalvoltage has a minimum magnitude threshold for phasor vectors of changein the secondary fundamental current.
 11. The apparatus of claim 11 inwhich the minimum magnitude threshold has a fixed value.
 11. Theapparatus of claim 11 in which the minimum magnitude threshold isdetermined by an algorithm that adapts the minimum magnitude thresholdbased on a history of measurements.
 10. The apparatus of claim 10 inwhich the algorithm to calculate the transformer fundamental vectorimpedance from the plurality of phasor vectors of change in secondaryfundamental current and the plurality of simultaneous phasor vectors ofchange in the secondary fundamental voltage comprises statisticalcorrelation between change in secondary fundamental current and changein secondary fundamental voltage.
 14. The apparatus of claim 14 in whichstatistical weighting is applied in such a way that changes in secondaryfundamental current with larger magnitudes receive more weight.